Parallel modular exponentiation using load balancing without precomputation

The modular exponentiation operation of the current algorithms for asymmetric cryptography is the most expensive part in terms of computational cost. The RSA algorithm, for example, uses the modular exponentiation algorithm in encryption and decryption procedure. Thus, the overall performance of those asymmetric cryptosystems depends heavily on the performance of the specific algorithm used for modular exponentiation. This work proposes new parallel algorithms to perform this arithmetical operation and determines the optimal number of processors that yields the greatest speedup. The optimal number is obtained by balancing the processing load evenly among the processors. Practical implementations are also performed to evaluate the theoretical proposals.

► New parallel methods for calculating modular exponentiation are described.
► Load balancing techniques are employed to obtain the optimum number of processors.
► Practical implementations have confirmed our theoretical analysis.